M-ISOMETRIC TRANSFORMATIONS OF HILBERT-SPACE .1.

A model for operators satisfying the equation GRAPHICS is given as multiplication by e(i phi) on a Hilbert space whose inner product is defined in terms of periodic distributions and we relate this model theory for the case when m = 2 to a disconjugacy theory for a subclass of Toeplitz operators of the type studied by Boutet de Monvel and Guilliman, classical function theoretic ideas on the Dirichlet space, and the theory of nonstationary stochastic processes. This is presented in a series of three papers. In this first paper, we concentrate on a model for these T.